FE based micromagnetic simulations of heterogeneous structures
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Cutting edge permanent magnetic materials such as neodymium-iron-boron (NdFeB) magnets play a crucial role in pushing the efficiency of power conversion devices, including wind turbines, sensors and electric motors to their limits, cf. [1]. Their huge potential to strongly influence current technological and social challenges such as the reduction of carbon dioxide emissions, provides a wide field of research, as their general increase in performance, the substitution of critical elements by harmless substances and the reduction of their required production energy. Here, microstructure engineering offers a promising approach, i.e., targeted influencing of sub-grain structures as grain boundaries or defects, to locally improve the magnetic properties. Thereby, finite element based micromagnetic simulations can be a strong technique to predict the magnetization behavior on fine scales. The FEM is characterized by a particularly flexible and not necessarily regular discretization, which is an advantage compared to other numerical methods for the discretization of heterogeneous microstructures, cf. [2]. The evolution of the magnetization vectors is determined by Gilbert's equation, which merely allows rotations, but no changes in length, cf. [3]. This constraint is enforced via a condensed perturbed Lagrange multiplier, cf. [4]. Within this contribution high-resolution micromagnetic simulations of strongly heterogeneous magnetic microstructures are presented. Thereby, the focus remains on analyzing the influence of grain boundary layers and inhomogeneities within the bulk material that often act as weak spots enabling premature reversal. [1] O. Gutfleisch, M.A. Willard, E. Brück, C.H. Chen, S.G. Sankar and J.P. Liu. Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient. Advanced Materials, 23:821-842, 2011. [2] A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez and B. Van Waeyenberge. The design and verification of MuMax3. AIP Advances, 4:107133, 2014. [3] A. Prohl. Computational Micromagnetism. Computational Material Science, 1st Edit., Springer, 2001. [4] M. Reichel and R. Niekamp and J. Schröder. Efficient micromagnetic-elastic simulations based on a perturbed Lagrangian function. Journal of Applied Physics, 134:103901, 2023.